Why Read the Originals?
In an age of accessible popular science books and online explanations, why struggle through Alan Turing’s original papers? The answer lies in the unique insight you gain from encountering a great mind’s ideas in their original form. Turing’s writings reveal not just what he discovered but how he thought: his logical precision, his clarity in addressing complex problems, and his ability to anticipate objections and alternative approaches. Reading Turing’s papers connects you directly to the moment these revolutionary ideas first emerged.
But Turing’s papers aren’t easy. Written for professional mathematicians and scientists of the 1930s-1950s, they assume significant background knowledge and use notation that may seem unfamiliar to modern readers. They reward careful study but can frustrate casual reading. This guide aims to make Turing’s most important writings more accessible, explaining which papers to start with, what background knowledge helps, and how to extract their essential insights.
Understanding Turing’s original writings deepens appreciation for his genius and reveals how foundational ideas in computing, artificial intelligence, and cryptography were first conceived. His papers remain surprisingly readable compared to much technical writing, thanks to his clear prose and logical organization.
Essential Background: What You Need to Know First
Before diving into Turing’s papers, certain background knowledge makes the experience far more rewarding:
Mathematical Maturity
You don’t need advanced mathematics for most of Turing’s papers, but you do need mathematical thinking: comfort with logical arguments, the ability to follow step-by-step reasoning, and patience with abstract concepts. Turing’s proofs are generally more accessible than those in pure mathematics papers because he’s often proving things about concrete computational processes.
Basic Logic and Set Theory
Understanding propositions, logical operators (AND, OR, NOT), and basic set notation (membership, union, intersection) helps significantly. Turing uses these as his fundamental tools for describing computational processes.
Historical Context
Knowing what problems Turing was addressing makes his papers far more meaningful. His 1936 paper responded to Hilbert’s Entscheidungsproblem. His wartime work addressed the Enigma machine’s cryptographic challenge. His 1950 paper engaged with philosophical debates about machine intelligence. Understanding these contexts reveals why Turing made the choices he did.
Patience with Notation
Turing uses notation that differs from modern conventions. His Turing machine descriptions use tables and symbols that look strange to readers familiar with modern programming languages. Rather than trying to translate everything immediately, try to understand the underlying concepts first, then work through the notation.
Paper 1: “On Computable Numbers” (1936)
This is Turing’s most important theoretical paper, introducing the Turing machine and proving fundamental results about the limits of computation.
How to Approach It
Start with Section 1, where Turing introduces “computing machines” (now called Turing machines). He describes them in remarkably clear prose before introducing formal notation. Pay special attention to his explanation of what it means for a number to be “computable.”
Section 2 contains the formal definitions. Don’t get bogged down in every detail on first reading. Understand that he’s describing:
- A tape divided into squares
- A scanning head that reads and writes symbols
- A finite set of states
- Rules determining what to do based on current state and symbol read
The examples in Sections 3-4 are crucial. Turing walks through specific machines, showing how simple rules can compute specific numbers. Work through at least one example carefully, following the machine’s operation step by step. This makes the abstract definition concrete.
Section 8 introduces the universal machine, arguably the paper’s most important concept. This machine can simulate any other machine by reading its description from the tape. This is the theoretical basis for programmable computers. The technical details are dense, but the concept itself is profound and worth grasping.
The later sections prove that the Entscheidungsproblem is unsolvable and introduce the halting problem. These are sophisticated mathematical arguments, but even a partial understanding reveals how Turing established fundamental limits on computation.
What to Take Away
You should emerge understanding:
- What a Turing machine is conceptually (even if you can’t reproduce all the notation)
- Why the universal machine matters (one machine can run any program)
- That there are problems no algorithm can solve (the halting problem being the classic example)
- How Turing defined “computation” precisely, enabling rigorous proofs about its limits
Paper 2: “The Prof’s Book on Enigma” (1940s)
During World War II, Turing wrote extensive documentation about Enigma and methods for breaking it. The Prof’s Book: Alan Turing’s Treatise on the Enigma presents Turing’s original typewritten manuscript with his handwritten notes and corrections, offering unique insight into his wartime codebreaking work.
How to Approach It
This manuscript differs dramatically from Turing’s published papers. It’s a practical technical document explaining how Enigma worked and how to attack it, written for the codebreakers at Bletchley Park, not for academic publication.
Start with the sections describing the Enigma machine itself. Turing explains:
- The rotor mechanism and how it scrambles letters
- The plugboard adding extra complexity
- Why the machine’s reciprocal property (if A encrypts to B, then B encrypts to A) creates a weakness
Understanding the machine’s operation is essential before grasping the cryptanalytic methods. Take time to work through examples of how a message gets encrypted.
The sections on breaking Enigma explain Turing’s logical approach: identifying patterns that survive encryption, using probable words (“cribs”), and how the Bombe machine mechanically tested possible rotor positions. The mathematical rigor is less formal than in his theoretical papers but the logical thinking is just as sharp.
What to Take Away
You should understand:
- How the Enigma machine’s mechanical design created both strength and weakness
- The logical reasoning behind Turing’s cryptanalytic methods
- How theoretical thinking about computation informed practical codebreaking
- The documentation style of a working scientist solving real-world problems under pressure
Paper 3: “Computing Machinery and Intelligence” (1950)
This is Turing’s most accessible and engaging paper, addressing the question “Can machines think?” It requires minimal mathematical background and is written in a conversational style with hypothetical dialogues.
How to Approach It
This paper is best read straight through like an essay. Turing structures it beautifully:
Section 1 introduces the “imitation game” (now called the Turing test): a human interrogator tries to distinguish between a human and a machine through text-based conversation. If the machine can fool the interrogator, Turing argues, we should consider it intelligent.
Sections 2-4 address objections to the possibility of machine intelligence. Turing presents each objection fairly, then dismantles it with logical precision and occasional wit. These sections reveal Turing’s philosophical sophistication and his ability to anticipate counterarguments.
The objections include:
- The theological objection: Only humans have souls capable of thought
- The mathematical objection: Gödel’s theorem shows machines have limitations
- The argument from consciousness: Machines can’t truly feel or understand
- Lady Lovelace’s objection: Machines can only do what we program them to do
Turing’s responses are models of clear philosophical reasoning. He doesn’t claim to prove machines can think but shows that objections to the possibility don’t hold up under scrutiny.
Section 7 discusses learning machines, anticipating modern machine learning. Turing proposes that instead of programming all knowledge, we should program machines that can learn from experience, like children learning from education.
What to Take Away
You should understand:
- The Turing test as a pragmatic approach to defining machine intelligence
- Why traditional objections to machine thinking are problematic
- Turing’s vision of machines that learn rather than merely executing fixed programs
- How philosophical questions about consciousness and intelligence connect to computing
Tips for Reading Turing’s Mathematical Notation
Turing’s notation can seem daunting, but a few strategies help:
Focus on the Concepts First
Before getting lost in symbols, understand what Turing is trying to express. He usually explains concepts in prose before formalizing them mathematically. Read the prose explanations carefully; they often contain the essential insight.
Work Through Examples
Turing provides examples for good reason. They make abstract definitions concrete. When you encounter a formal definition, immediately look for examples and work through them step by step. This builds intuition that makes later technical material more approachable.
Translate to Familiar Notation
If you’re comfortable with modern programming languages, try translating Turing’s machine descriptions into pseudocode or even working code. A Turing machine specification is essentially a program, and rewriting it in familiar notation can clarify its operation.
Don’t Aim for Complete Mastery
You can gain tremendous value from Turing’s papers without understanding every technical detail. Grasp the main arguments and key insights. The technical machinery supports these insights, but you don’t need to reproduce every proof to understand their significance.
Turing’s Writing Style: Clarity and Precision
One advantage of reading Turing is his remarkably clear writing. Unlike many technical authors, Turing writes prose that’s precise but not needlessly complex. He uses concrete examples, anticipates reader confusion, and structures arguments logically.
His 1950 paper on machine intelligence is particularly accessible, using conversational language and even humor. When addressing the objection that machines lack consciousness, he quips: “I do not wish to give the impression that I think there is no mystery about consciousness…But I do not think these mysteries necessarily need to be solved before we can answer the question with which we are concerned in this paper.”
This combination of philosophical depth and clear expression makes Turing’s papers surprisingly enjoyable to read, especially compared to much academic writing. His goal was always to communicate ideas clearly, not to impress with complex jargon.
Resources to Support Your Reading
Several resources can enhance your study of Turing’s writings:
The Annotated Turing by Charles Petzold provides a detailed line-by-line commentary on the 1936 paper, explaining every concept and piece of notation. It’s ideal for readers wanting deep understanding of the technical content.
Alan Turing: His Work and Impact collects Turing’s papers with modern commentaries by leading computer scientists, providing historical context and explaining significance.
The Essential Turing edited by Jack Copeland includes major papers plus biographical material, offering a comprehensive introduction to Turing’s work across different fields.
For Turing’s wartime work, The Prof’s Book: Alan Turing’s Treatise on the Enigma provides access to his actual manuscript, complete with handwritten annotations, showing how Turing documented his codebreaking methods for colleagues at Bletchley Park.
Why Turing’s Papers Still Matter
Reading Turing’s original writings offers more than historical interest. His papers remain relevant because:
Foundational concepts persist: The Turing machine remains the standard model for theoretical computer science. Every complexity class, every computability proof, traces back to Turing’s 1936 framework.
Philosophical questions endure: His 1950 paper poses questions about machine intelligence that we’re still grappling with as AI becomes more sophisticated. The Turing test, while debated, remains a landmark thought experiment.
Logical thinking transcends eras: Turing’s method of precisely defining terms, systematically addressing objections, and constructing rigorous proofs exemplifies clear thinking that’s timeless.
Inspiration and perspective: Seeing how Turing worked through foundational problems, often with minimal precedent to build on, inspires modern researchers facing new challenges. His willingness to question assumptions and think from first principles remains a model.
Direct Access to a Revolutionary Mind
Reading Alan Turing’s original papers requires effort, but the rewards are substantial. You gain direct access to the thinking that created theoretical computer science, broke Nazi codes, and posed questions about machine intelligence that remain central today. His clear prose, logical precision, and profound insights make the effort worthwhile.
Start with the 1950 paper on machine intelligence if you want accessibility. Tackle the 1936 paper on computable numbers if you want to understand computation’s theoretical foundations. Explore The Prof’s Book to see how Turing applied theoretical thinking to practical wartime problems.
Don’t aim for complete mastery on first reading. Engage with the main arguments, work through key examples, and absorb the overall vision. Return later for deeper understanding as your knowledge grows. Turing’s papers reward multiple readings, revealing new insights each time.
In an age of secondary sources and popularizations, reading the originals connects you to ideas at their source. You see not just what Turing discovered but how he thought, how he structured arguments, and how he communicated revolutionary concepts. This direct engagement with a great mind’s work is irreplaceable, offering insights no summary can capture. Turing’s papers remain vibrant documents that continue to shape how we think about computation, intelligence, and the possibilities of machines.
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